Mechanical response of wrinkled structures

Surface wrinkling of compressed thin films on soft substrates has been of great interest both in fundamental studies and in practical applications. While the formation and evolution of wrinkled structures is well understood, much less is known about how wrinkled surfaces respond to external forces. In this talk, I will discuss how wrinkled structures respond to an infinitesimal point force. We find that the linear response diverges near the onset of the wrinkling instability and that it decays away from this critical threshold, where wrinkles are fully developed. Furthermore, we find that the dominant response comes from the Fourier modes that correspond to the wavelength of wrinkles. In analogy with the critical phenomena in ferromagnets, we can introduce critical exponents for the mechanical response of wrinkled structures, which are consistent with the Landau theory. Finally, I will also comment on how to use this theory to study the response of wrinkled structures to more complicated distributions of external forces, such as the interaction of wrinkled surfaces with liquid droplets.